Roasted butternut squash
1 cup peeled and cubed butternut squash (1/2-inch cubes)
2 tbsp. olive oil
1 tbsp. thyme
Kosher salt and black pepper, to taste
Chilies, filling and garnish
5 poblano chilies
2 cups dry quinoa, cooked according to package directions
2 cups shredded Oaxaca cheese (or substitute mozzarella)
2 cups shredded Manchego cheese (option: reserve 1/2 cup to sprinkle on top of chilies)
2 tsp. chopped chives
Mexican crema, for garnish (or substitute sour cream)
8 cups instant corn masa flour such as Maseca (or substitute cornmeal)
1/2 cup vegetable oil
For roasted butternut squash: Preheat oven to 325 degrees. Toss squash cubes with oil, thyme, salt and pepper. Place in a roasting pan. Cover with foil and roast for 45 minutes. Remove and set aside.
For chilies: Reduce oven temperature to 300 degrees. Roast poblano chilies for 15 minutes, then remove skin (or char on gas burner, see below). With a paring knife, make a slit across the top of chili just below stem, leaving stem intact. Starting from middle of slit, slice lengthwise down to the tip of the pepper, taking care to cut through one layer only. Open chili like a book and pull out seeds and inner membranes. (You may need to use a paring knife to loosen the top of the seedpod.) Repeat with remaining chilies and set aside.
To assemble: Mash roasted squash, quinoa, cheeses and chives together and separate into 5 balls. Press each ball of filling inside chilies. If you reserved 1/2 cup cheese, sprinkle cheese on top of each filling. Close each chili and use hands to form back to chili shape.
Line up 4 pans, left to right. In the first pan, put half of the corn masa flour. In the second, break open the eggs and whip with a fork. In the third, put the other half of corn masa flour. The fourth pan is for placing the finished chilies.
Working from left to right, place a chili in the first pan and roll in corn masa flour until well-coated. Place in second pan until coated with egg and then into third pan in corn masa flour. Press flour firmly onto the chili, working to retain the chili's shape. Set in the fourth pan. Repeat with all chilies. Let sit for 2 to 3 minutes.
Heat about 1 inch vegetable oil in a deep skillet over medium-high heat until a deep-fry thermometer registers 375 degrees.
Add chilies to hot oil, 1 or 2 at a time; fry, flipping once with tongs, until golden, 1 to 2 minutes per side. Drain on paper towels. Garnish with Mexican crema or sour cream.
Note for gas-burner cooking: Turn burner on high. Char chilies on the burner grate, turning with tongs until blackened all over. Let soften. Transfer chilies to a heavy-duty resealable plastic bag and close. Let stand 10 minutes. The chilies will steam in the bag, making them soft and easy to peel. Gently rub chilies with paper towels to remove as much skin as possible. It's OK if a few flecks remain; they'll add flavor, so do not rinse.